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Home » Classroom Facts That Teacher Memes Get Wrong – Everyone Needs to See This! - Abu Waleed Tea

Classroom Facts That Teacher Memes Get Wrong – Everyone Needs to See This! - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Simplify \( \frac{3 + 2i}{4 - i} \) and express in rectangular form.

📌 Multiply numerator and denominator by conjugate \( 4 + i \):

📌 Numerator: \( (3 + 2i)(4 + i) = 12 + 3i + 8i + 2i^2 = 12 + 11i - 2 = 10 + 11i \)

📌 Denominator: \( (4 - i)(4 + i) = 16 + 1 = 17 \)

📌 Result: \( \frac{10 + 11i}{17} = \frac{10}{17} + \frac{11}{17}i \)

📌 #### \( \frac{10}{17} + \frac{11}{17}i \)

📌 A rectangular prism has a volume of 108 cubic meters. Its length is twice its height, and its width is 3 meters more than its height. Find the dimensions.

📌 Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \).

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\text{Average} = \frac{3.75 + 8.25}{2} = \frac{12}{2} = \boxed{6}
Question: What is the smallest prime factor of $ 1211 $?
Solution: To find the smallest prime factor of 1211, we test divisibil...
\div 7 \approx 173 \quad \text{(not an integer)}
Test divisibility by 11:
Try dividing directly:
\div 1211 = 1 \quad \text{and 1211 is prime?}
Check divisibility by primes up to $ \sqrt{1211} \approx 34.8 $. Conti...
Not divisible by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, or 31.
Since none of these divide 1211, it is a prime number. Therefore, the...

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